We present an investigation into the use of an explicitly correlated plane wave basis for periodic wavefunction expansions at the level of second-order Møller-Plesset (MP2) perturbation theory. The convergence of the electronic correlation energy with respect to the one-electron basis set is investigated and compared to conventional MP2 theory in a finite homogeneous electron gas model. In addition to the widely used Slater-type geminal correlation factor, we also derive and investigate a novel correlation factor that we term Yukawa-Coulomb. The Yukawa-Coulomb correlation factor is motivated by analytic results for two electrons in a box and allows for a further improved convergence of the correlation energies with respect to the employed basis set. We find the combination of the infinitely delocalized plane waves and local short-ranged geminals provides a complementary, and rapidly convergent basis for the description of periodic wavefunctions. We hope that this approach will expand the scope of discrete wavefunction expansions in periodic systems.
REFERENCES
1.
A. J.
Cohen
, P.
Mori-Sánchez
, and W.
Yang
, Chem. Rev.
112
, 289
(2012
).2.
G. H.
Booth
, A.
Grüneis
, G.
Kresse
, and A.
Alavi
, Nature (London)
493
, 365
(2013
).3.
P.
Ayala
, K.
Kudin
, and G.
Scuseria
, J. Chem. Phys.
115
, 9698
(2001
).4.
H.
Stoll
, B.
Paulus
, and P.
Fulde
, J. Chem. Phys.
123
, 144108
(2005
).5.
L.
Maschio
, D.
Usvyat
, F. R.
Manby
, S.
Casassa
, C.
Pisani
, and M.
Schütz
, Phys. Rev. B
76
, 075101
(2007
).6.
S.
Casassa
, M.
Halo
, L.
Maschio
, C.
Roetti
, and C.
Pisani
, Theor. Chem. Acc.
117
, 781
(2007
).7.
M.
Marsman
, A.
Grüneis
, J.
Paier
, and G.
Kresse
, J. Chem. Phys.
130
, 184103
(2009
).8.
S. J.
Nolan
, M. J.
Gillan
, D.
Alfè
, N. L.
Allan
, and F. R.
Manby
, Phys. Rev. B
80
, 165109
(2009
).9.
A.
Grüneis
, M.
Marsman
, and G.
Kresse
, J. Chem. Phys.
133
, 074107
(2010
).10.
S. J.
Binnie
, S. J.
Nolan
, N. D.
Drummond
, D.
Alfè
, N. L.
Allan
, F. R.
Manby
, and M. J.
Gillan
, Phys. Rev. B
82
, 165431
(2010
).11.
S. J.
Nolan
, P. J.
Bygrave
, N. L.
Allan
, and F. R.
Manby
, J. Phys.: Condens. Matter
22
, 074201
(2010
).12.
A.
Grüneis
, G. H.
Booth
, M.
Marsman
, J.
Spencer
, A.
Alavi
, and G.
Kresse
, J. Chem. Theory Comput.
7
, 2780
(2011
).13.
D.
Usvyat
, B.
Civalleri
, L.
Maschio
, R.
Dovesi
, C.
Pisani
, and M.
Schutz
, J. Chem. Phys.
134
, 214105
(2011
).14.
H.
Stoll
and K.
Doll
, J. Chem. Phys.
136
, 074106
(2012
).15.
C.
Mueller
and B.
Paulus
, Phys. Chem. Chem. Phys.
14
, 7605
(2012
).16.
M.
Del Ben
, J.
Hutter
, and J.
VandeVondele
, J. Chem. Theory Comput.
8
, 4177
(2012
).17.
P. J.
Bygrave
, N. L.
Allan
, and F. R.
Manby
, J. Chem. Phys.
137
, 164102
(2012
).18.
K.
Burke
and L. O.
Wagner
, Int. J. Quantum Chem.
113
, 1601
(2013
).19.
W. M. C.
Foulkes
, L.
Mitas
, R. J.
Needs
, and G.
Rajagopal
, Rev. Mod. Phys.
73
, 33
(2001
).20.
T.
Kato
, Commun. Pure Appl. Math.
10
, 151
(1957
).21.
R. T.
Pack
and W.
Byers Brown
, J. Chem. Phys.
45
, 556
(1966
).22.
A.
Carlsson
and N.
Ashcroft
, Phys. Rev. B
25
, 3474
(1982
).23.
X.-Y.
Pan
and V.
Sahni
, J. Chem. Phys.
119
, 7083
(2003
).24.
D. P.
Tew
, J. Chem. Phys.
129
, 014104
(2008
).25.
S.
Boys
, Proc. R. Soc. London, Ser. A
258
, 402
(1960
).26.
S.
Boys
and N.
Handy
, Proc. R. Soc. London, Ser. A
310
, 43
(1969
).27.
W.
Kutzelnigg
, Theor. Chim. Acta
68
, 445
(1985
).28.
W.
Klopper
and W.
Kutzelnigg
, Chem. Phys. Lett.
134
, 17
(1987
).29.
W.
Kutzelnigg
and W.
Klopper
, J. Chem. Phys.
94
, 1985
(1991
).30.
C.
Hättig
, W.
Klopper
, A.
Köhn
, and D. P.
Tew
, Chem. Rev.
112
, 4
(2012
).31.
L.
Kong
, F. A.
Bischoff
, and E. F.
Valeev
, Chem. Rev.
112
, 75
(2012
).32.
D. P.
Tew
, C.
Hättig
, R. A.
Bachorz
, and W.
Klopper
, in Recent Progress in Coupled Cluster Methods – Theory and Applications
, edited by P.
Čársky
, J.
Paldus
, and J.
Pittner
(Springer
, Dordrecht
, 2010
), pp. 535
–572
.33.
H.-J.
Werner
, T. B.
Adler
, G.
Knizia
, and F. R.
Manby
, in Recent Progress in Coupled Cluster Methods – Theory and Applications
, edited by P.
Čársky
, J.
Paldus
, and J.
Pittner
(Springer
, Dordrecht
, 2010
), pp. 573
–620
.34.
S.
Ten-no
and J.
Noga
, WIREs Comput. Mol. Sci.
2
, 114
(2012
).35.
S.
Ten-no
, Theor. Chem. Acc.
131
, 1070
(2012
).36.
T.
Shiozaki
and S.
Hirata
, J. Chem. Phys.
132
, 151101
(2010
).37.
W.
Klopper
and C. C. M.
Samson
, J. Chem. Phys.
116
, 6397
(2002
).38.
E. F.
Valeev
, Chem. Phys. Lett.
395
, 190
(2004
).39.
S.
Kedžuch
, M.
Milko
, and J.
Noga
, Int. J. Quantum Chem.
105
, 929
(2005
).40.
S.
Ten-no
, J. Chem. Phys.
121
, 117
(2004
).41.
H.-J.
Werner
, T. B.
Adler
, and F. R.
Manby
, J. Chem. Phys.
126
, 164102
(2007
).42.
D. P.
Tew
and W.
Klopper
, Mol. Phys.
108
, 315
(2010
).43.
A.
May
, E.
Valeev
, R.
Polly
, and F.
Manby
, Phys. Chem. Chem. Phys.
7
, 2710
(2005
).44.
S.
Ten-no
, Chem. Phys. Lett.
398
, 56
(2004
).45.
D. P.
Tew
and W.
Klopper
, J. Chem. Phys.
123
, 074101
(2005
).46.
K. E.
Yousaf
and K. A.
Peterson
, J. Chem. Phys.
129
, 184108
(2008
).47.
F. A.
Bischoff
, S.
Wolfsegger
, D. P.
Tew
, and W.
Klopper
, Mol. Phys.
107
, 963
(2009
).48.
49.
D. P.
Tew
, B.
Helmich
, and C.
Haettig
, J. Chem. Phys.
135
, 074107
(2011
).50.
T. B.
Adler
and H.-J.
Werner
, J. Chem. Phys.
135
, 144117
(2011
).51.
R. J.
Gdanitz
, Chem. Phys. Lett.
210
, 253
(1993
).52.
S.
Ten-no
, Chem. Phys. Lett.
447
, 175
(2007
).53.
T.
Shiozaki
and H.-J.
Werner
, J. Chem. Phys.
131
, 141103
(2010
).54.
T.
Shiozaki
, G.
Knizia
, and H.-J.
Werner
, J. Chem. Phys.
134
, 034113
(2011
).55.
T.
Shiozaki
and H.-J.
Werner
, J. Chem. Phys.
134
, 184104
(2011
).56.
S.
Kedžuch
, O.
Demel
, J.
Pittner
, S.
Ten-no
, and J.
Noga
, Chem. Phys. Lett.
511
, 418
(2011
).57.
R.
Haunschild
, S.
Mao
, D.
Mukherjee
, and W.
Klopper
, Chem. Phys. Lett.
531
, 247
(2012
).58.
M.
Torheyden
and E. F.
Valeev
, J. Chem. Phys.
131
, 171103
(2009
).59.
L.
Kong
and E. F.
Valeev
, J. Chem. Phys.
135
, 214105
(2011
).60.
L.
Kong
and E. F.
Valeev
, J. Chem. Phys.
133
, 174126
(2010
).61.
G. H.
Booth
, D.
Cleland
, A.
Alavi
, and D. P.
Tew
, J. Chem. Phys.
137
, 164112
(2012
).62.
T.
Shiozaki
and H.-J.
Werner
, Mol. Phys.
111
, 607
(2013
).63.
J. J.
Shepherd
, A.
Grüneis
, G. H.
Booth
, G.
Kresse
, and A.
Alavi
, Phys. Rev. B
86
, 035111
(2012
).64.
W.
Kutzelnigg
and J.
Morgan
, J. Chem. Phys.
96
, 4484
(1992
).65.
A.
Grüneis
, M.
Marsman
, J.
Harl
, L.
Schimka
, and G.
Kresse
, J. Chem. Phys.
131
, 154115
(2009
).66.
J. J.
Shepherd
, G.
Booth
, A.
Grüneis
, and A.
Alavi
, Phys. Rev. B
85
, 081103
(2012
).67.
J. J.
Shepherd
, G. H.
Booth
, and A.
Alavi
, J. Chem. Phys.
136
, 244101
(2012
).68.
J. J.
Shepherd
and A.
Grüneis
, Phys. Rev. Lett.
110
, 226401
(2013
).69.
A.
Roggero
, A.
Mukherjee
, and F.
Pederiva
, “Quantum Monte Carlo with coupled-cluster wave functions
,” e-print arXiv:1304.1549 (unpublished).70.
D. M.
Ceperley
and B. J.
Alder
, Phys. Rev. Lett.
45
, 566
(1980
).71.
J. P.
Perdew
and A.
Zunger
, Phys. Rev. B
23
, 5048
(1981
).72.
C.
Moller
and M.
Plesset
, Phys. Rev.
46
, 0618
(1934
).73.
R. A.
Bachorz
, F. A.
Bischoff
, A.
Glöß
, C.
Hättig
, S.
Höfener
, W.
Klopper
, and D. P.
Tew
, J. Comput. Chem.
32
, 2492
(2011
).74.
D. P.
Tew
and W.
Klopper
, J. Chem. Phys.
125
, 094302
(2006
).75.
J.
Noga
, S.
Kedžuch
, J.
Šimunek
, and S.
Ten-no
, J. Chem. Phys.
128
, 174103
(2008
).76.
G.
Kresse
and J.
Furthmuller
, Phys. Rev. B
54
, 11169
(1996
).77.
F.
Gygi
and A.
Baldereschi
, Phys. Rev. B
34
, 4405
(1986
).78.
T.
Gaskell
, Proc. Phys. Soc. London
77
, 1182
(1961
).79.
D.
Ceperley
, Phys. Rev. B
18
, 3126
(1978
).80.
N.
Umezawa
and S.
Tsuneyuki
, Phys. Rev. B
69
, 165102
(2004
).81.
S. R.
Chinnamsetty
, H.
Luo
, W.
Hackbusch
, H.-J.
Flad
, and A.
Uschmajew
, Chem. Phys.
401
, 36
(2012
).82.
K.
Schmidt
and J.
Moskowitz
, J. Chem. Phys.
93
, 4172
(1990
).83.
D.
Ceperley
and B.
Alder
, J. Chem. Phys.
81
, 5833
(1984
).84.
J.
Toulouse
and C. J.
Umrigar
, J. Chem. Phys.
128
, 174101
(2008
).85.
P. E.
Hoggan
, Int. J. Quantum Chem.
113
, 277
(2013
).86.
P. M. W.
Gill
and P.-F.
Loos
, Theor. Chem. Acc.
131
, 1069
(2011
).87.
P.-F.
Loos
and P. M. W.
Gill
, J. Chem. Phys.
138
, 164124
(2013
).88.
J.
Noga
and W.
Kutzelnigg
, J. Chem. Phys.
101
, 7738
(1994
).89.
D. P.
Tew
, W.
Klopper
, C.
Neiss
, and C.
Hättig
, Phys. Chem. Chem. Phys.
9
, 1921
(2007
).90.
T. B.
Adler
, G.
Knizia
, and H.-J.
Werner
, J. Chem. Phys.
127
, 221106
(2007
).91.
G. H.
Booth
, A. J. W.
Thom
, and A.
Alavi
, J. Chem. Phys.
131
, 054106
(2009
).92.
G. H.
Booth
, D.
Cleland
, A. J. W.
Thom
, and A.
Alavi
, J. Chem. Phys.
135
, 084104
(2011
).93.
D.
Cleland
, G. H.
Booth
, C.
Overy
, and A.
Alavi
, J. Chem. Theory Comput.
8
, 4138
(2012
).94.
D.
Cleland
, G. H.
Booth
, and A.
Alavi
, J. Chem. Phys.
132
, 041103
(2010
).© 2013 AIP Publishing LLC.
2013
AIP Publishing LLC
You do not currently have access to this content.